Imaginary Numbers Are Real [Part 1: Introduction]

Today I'm excited to release part one of my summer project: a YouTube series entitled "Imaginary Numbers are Real". I'll be releasing parts each Friday, starting today, and ending on October 23.

About the Series

Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space.  Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.

In this ten part YouTube series, we'll explore the origins, storied development, and fascinating applications of imaginary numbers. We'll focus on the how, and more importantly, the why behind what may be the murkiest subject in high school mathematics. This series is appropriate for anyone from the high school to graduate school level and beyond who is interested in (or required to be interested in) imaginary numbers.


1. Introduction
2. A Little History
3. Cardan's Problem
4. Bombelli's Solution
5. Numbers are Two Dimensional
6. The Complex Plane
7. Math Wizardry
8. Closure
9. Complex Functions
10. Applications


Like most mathematics, passive listening will only get you so far - you really need to work with imaginary numbers to develop a full understanding. This series is accompanied by a workbook that includes guided notes for each video, additional fun stuff that didn't make it into the videos, exercises with solutions, and a test that covers the entire topic. This is a great way for individuals to develop a deeper grasp of the material, and an excellent resource for educators at the high school or college level. The workbook will be available October 23, 2015 - you can preorder now to ensure you receive a workbook from the first limited print run.

Liner Notes

I had a great time creating this series - it's funny, I actually set out to create a series on the Fourier Transform (which I still plan to do), researching this led me to the fascinating Euler's formula and identity, which ultimately led me all the way down to imaginary numbers. I've been using imaginary numbers for over a decade, but never really questioned where they came from, why we need them, or why they're so ubiquitous in engineering. What I found really fascinated me, and really served to remind me how deep and profound the connection between mathematics and reality is. Imaginary numbers are just an abstract concept that basically fall out of algebra, but turn out be essential in describing real world processes. It's ironic that zero, negative, and imaginary numbers were resisted for so long precisely because they don't seem directly connected to anything in the real world - but once we take the leap of faith and accept these guys, we find ourselves with incredible tools are essential in describing complex real world phenomena.

The production for this series gave me a run for my money! I had the idea of the "pulling the function out of the page" shot early on- but I had no idea how much work it would take! I built a custom 4 axis camera rig, wrote custom python code to control it, learned how to 3d animate in Cinema 4d, and how to composite (and what compositing is) with Adobe After Effects. All this was a blast, but took a huge amount of time and gave me even more respect for folks who make films.

Close up of camera rig for shooting motion shots.

Four axis camera rig I built this summer. 

Finally, if you're really paying attention, you may see that I'm wearing a ring in some shots, but not in others - that's because I got married to my wonderful wife Alison as I was finishing shooting part one.

Summer reading...